Question

How much money should be deposited today in an account that earns 7% compounded semiannually so that it will accumulate to $12,000 in four years?

Answer 1

Given rate is = 7% or 0.07

Total amount needed = $12000

Time = 4 years

Here, the  deposit is  compounded semiannually, means twice per year and this gives 8 annual compounding periods in 4 years.

The equation becomes:

P= $\frac{12000}{(1+\frac{0.07}{2})^{2.4}}$

P = $\frac{12000}{1.035^{8}}$

Solving it, we get P = $ 9112.93

Hence $9112.93 should be deposited today.